Taliessin’s look darkened; his hand shook
while he touched the dragons; he said ‘We had a good thought.
Sir, if you made verse you would doubt symbols.
I am afraid of the little loosed dragons.
When the means are autonomous, they are deadly; when words
escape from verse they hurry to rape souls;
when sensation slips from intellect, expect the tyrant;
the brood of carriers levels the good they carry.
We have taught our images to be free; are we glad?
are we glad to have brought convenient heresy to Logres?’
(Charles Williams, “Bors to Elayne: on the King’s Coins” , in Taliessin Through Logres, 1930)
The stimulus for the following piece of wittering is that I recently spent a couple of hours browsing round James Atherton’s excellent pages on teaching and learning, and in particular his collection of heterodox opinions. One of the pieces that struck me — perhaps solely due to confirmation bias — was the article “Learning styles don’t matter” , which argues that there is little empirical evidence either that learning styles (as opposed to learning strategies) exist or that trying to accommodate them works. I don’t want to get into the merits of this particular topic, not least because Mr Atherton has done a much better job than I could. However, I think it serves as a nice illustration of a general question: given that educational theories do not (at least at present) have the same degree of solidity as theories in the natural sciences, how should we interpret and use them?
I grew up, and still do most of my thinking, at the liberal end of the reformed-Catholic strand of the Judaeo-Christian tradition: I’m not going to make exclusive claims for this tradition, but it does give you some useful ideas to work with when you’re dealing with concepts that are hard to pin down. I’m going to make a convenient but probably indefensible division of the ways we can view theories into three categories: as metaphors, as myths, and as a state religion.
Most of us — even mathematicians — have a reasonable idea what a metaphor is, but we may not appreciate how much of our everyday speech and writing is built round them, either explicitly or implicitly. Implicit metaphors seem to be particularly common when we try to discuss abstract concepts: in my first paragraph above, I see that I’ve referred to “trying to accommodate” learning styles (implicit: learning styles take up space and there is a finite region into which they must be fitted?) and to the “degree of solidity” of theories (implicit: theories provide a constraint of some form on our thinking or actions?).
Metaphors of this kind are practically indispensible for thought and so there’s no point railing against them per se. The danger can come when a particular implicit metaphor directs one’s thought more strongly than one had realised: I think this is the case, for example, with the “discovery” and “construction” metaphors applied to knowledge both in scientific and in educational contexts . (See especially Anna Sfard’s classic and eminently sane article “On two metaphors for learning and the dangers of choosing just one” .)
Myths are a more awkward topic, because the word has acquired strong pejorative overtones, but I’ll try to stick to my definition in an earlier post of a myth as “a story we tell in order to encapsulate a worldview or the kind of truth that has an imaginative dimension”. A myth is generally more complex than a metaphor, and what tends to be implicit about it is not its presence or absence but the kind of truth-value we assign to it — unlike a metaphor, a myth is generally presented as a statement that can be true or false. (For example, most people in the Western culture will be aware of the Genesis creation myth, but opinions as to its status include regarding it as literal truth; as a schematic diagram of the sequence of creation; as an imaginative encapsulation of the moral relationship between God, humankind and the rest of creation; or as an outdated and dangerous pre-scientific theory with nasty consequences for the societies that accept it.) I think it makes sense to borrow — and probably twist — a phrase of C. S. Lewis’s, and acknowledge the possibility of “true myths”, which simultaneously satisfy the natural criteria for literal accuracy and point beyond themselves to something not directly comprehensible in these terms. Lewis, as a committed Christian, took Jesus’s death and resurrection as the archetype of a true myth: the physical event occurred but also signified something — redemption — which cannot be phrased in terms of physical events. So far as my understanding of physics goes, I think one might argue that elementary particles are true myths in a very vaguely analogous sense.
In this sense, many (most?) educational theories can be seen as myths: learning styles; the construction of knowledge; the learning cycle… We can ask empirical questions about the evidence that supports their literal claims, and if it turns out that this evidence is poor then this rules out certain ways of reading these myths. (Given my enthusiasm for geology, it shouldn’t be hard to tell which possibilities I personally rule out for Genesis.) But it’s still possible to use them — or to abuse them — as a kind of imaginative tool that either exacerbates or corrects the deficiencies in our view of education.
In practice, I suspect most of us have a kind of “working mythology” in most things that we do. In that previous post, I argued that the working mythology of many scientists involves elements of the discovery metaphor, the “lone genius” myth and a realist or even Platonist philosophy, and that while all these elements can be attacked on philosophical or historical grounds, the mythology serves a purpose — it captures the sense that reality tends to push back against our theories, and that social consensus is not the essential determinant of scientific validity. (I think there are interesting things to be said about the working mythologies of mathematicians and, oddly enough, poets, and I hope to come back to this in a later post.) The working mythology of a teacher might be an orthodoxy such as radical constructivism or the theory of multiple intelligences; more probably, it is an eclectic mixture of ideas drawn from many incompatible theories. Orthodox mythologies, like systematic theologies, tend to have the virtue of intellectual coherence and the demerit of large blind spots. Eclectic mythologies, like syncretistic religions, can be internally contradictory or downright nonsensical, with Apollo and the Furies slugging it out to determine the rights and wrongs of an action; their virtue is that they give you a local deity to invoke in any situation without handing over your body and soul entire.
Looking at learning styles as a (not necessarily true) myth, what can we draw from it? The most obvious point is that it reminds us of the variations between students, and the different informal approaches that one can take to a concept. I’m not convinced that the question “how do I design my teaching to accommodate the visual, the aural and the kinaesthetic learner?” is much more sensible than constructing elaborate chronologies to reconcile the narratives in Genesis. I do think, though, that the question “if a visual / aural / kinaesthetic learner existed, how might they learn this topic?” can be a productive one. It may well make us aware of our own biases and force us to determine the extent to which these are personal preferences and the extent to which they’re intrinsic to the subject. At the very least, I find that it suggests occasional gimmicks that can be used to break up the normal routine of a class. (When I used to teach the fluid dynamics of flow round a wing, I discovered in this way that lobbing first a screwed-up sheet of A4 paper and then a paper aeroplane into the audience was a great way of waking them up briefly. It also means I can claim to have thrown more paper aeroplanes at my students than they have so far thrown at me.)
In a similar spirit, the constructivist myth, although it becomes absurd in the hands of fundamentalists, has its merits. In particular, it immediately proscribes the worship of a number of other idols, such as the passive–transmissive model of learning (more a straw figure than an idol, admittedly), or the mystical–revelatory model beloved of popular science writers who’ve read too much about Ramanujan. It also tends to stress the social context of learning, providing the teacher with tools to approach many group effects that more cognitively-oriented myths ignore. And, perhaps most importantly for a maths teacher, it opens the door to consider heuristics, the problem of didactical inversion and the relation between formal and informal images of mathematical concepts.
I could probably go on, but I think the basic point is fairly clear: partial or provisional commitment to a particular myth can be of benefit; and frankly, even a more fundamentalist commitment to an orthodoxy may at least stir one’s conscience to action in admirable ways. (I can’t subscribe to every detail of the theology of, say, the Salvation Army, but they do tough work in difficult situations I’d not have the guts to enter.)
When commitment to a myth becomes particularly dangerous is, I think, when it leads one not merely to proselytise for it but to compel other people to subscribe to it. At this point, when it is supported by institutional authority, the myth has become a state religion. In their literal form, the dangers of state religions are fairly widely known. All too often they’re bad both for the sanity of the state and the moral integrity of the religion: the state can avoid sensible debate around certain topics because they’re under the authority of the religion, while the religion can avoid challenge on these topics because its current wisdom is backed by raw power.
Unfortunately, there are plenty of opportunities for the myths of education to harden into state religions. I had to undergo one such when I did my teaching certificate, in a department in which radical constructivism had been established. One passed or failed the certificate mainly according to one’s ability to describe one’s activities in the language of radical constructivism; one’s prior knowledge or alternative approaches were automatically “theoretically naive”; and because there was no such thing as knowledge outside the heads of learners, disciplinary differences were merely an illusion held by the theoretically naive. (I caricature this baloney less than I’d like; after considerable outcry, some reform has taken place but I understand that large parts of this qualification remain more or less a waste of time.) By and large, the greater the extent to which teaching is regulated as part of a formal system of reward and punishment, the greater the temptation to establish a single religion with a single list of sins and virtues. It’s very objective (in the tick-box sense) and it provides a ready-made vocabulary of largely meaningless words, of the sort beloved of the Dilbertian management caste. The problem is exacerbated when politicians (professional or amateur) get involved, because a new or re-heated orthodoxy gives lots of opportunities for initiatives and radical reform and a great deal of implicitly blaming the teachers for everything that’s gone wrong in the past. Combine this with the observation that almost every innovation seems to work at first, and you get a recipe for a bewildering succession of one-true-faiths, each imposed by fire and the sword in a manner faintly reminiscent of the Thirty Years War or the evening after an Old Firm game in Glasgow.
So where does this leave the struggling classroom teacher, already far out at sea, being battered by competing storms, waves and cross-currents and with the sharks circling? While we’re unfortunate enough to live under state religions, some hypocrisy is probably necessary. I passed my teaching certificate by learning the language well enough to fake orthodoxy (and, admittedly, slipping in the occasional sarcastic touch I was fairly sure the markers wouldn’t understand). Sometimes we might have to rebel outright and take the consequences of declaring that the state religion is an abomination and a delusion. Somebody probably needs to do this, and on my braver days I sometimes think that one day it might be me. But if we have the freedom to do so, even if only inside our own heads, I think we need to cultivate an awareness of the metaphors of education and an ability to read the myths of education with a combination of imaginative engagement and intellectual agnosticism. This isn’t an attitude that comes naturally to a natural scientist or a mathematician, but I hope it can be done. Perhaps the most valuable aid, if we can cling on to it, is a working sense of humour; and having said that, maybe one of my favourite Jewish jokes might be a good note to end on.
A young man asked his rabbi, “What is Talmud?”
“Consider two men who climb inside a chimney,” said the rabbi. “One comes out clean, and the other comes out dirty. Which man washes himself?”
“I’m not sure,” admitted the young man.
“The clean one washes,” said the rabbi, “because he sees the dirty man, and thinks he must be dirty, too, whereas the dirty man sees the clean one, and thinks that he, too, must be clean. Now, two men climb inside a chimney. One comes out clean, and the other dirty. Which one washes?”
“The clean one,” answered the young man. “You just told me so.”
“The dirty one washes,” replied the rabbi. “Each man looks at himself. The clean one sees that he is clean, the dirty one sees that he is dirty, and the dirty one washes. Now, two men climb inside a chimney. One comes out clean, and the other dirty. Which one washes?”
“I guess it could be either one,” said the young man.
“They both wash,” replied the rabbi. “It is impossible that a man should climb inside a chimney and come out clean.”
“Now, wait a minute,” challenged the young man. “You’ve just given me three contradictory answers to the same question. That’s impossible!”
“No,” said the rabbi. “That’s Talmud.”
That’s education, too.